Soft learning vector quantization and clustering algorithms based on reformulation

Proposes a methodology that reduces the development of soft learning vector quantization (LVQ) and clustering algorithms to the minimization of an admissible reformulation function using gradient descent. The search for admissible reformulation functions reduces to the selection of admissible generator functions. Linear and exponential generator functions result in existing fuzzy LVQ and and clustering algorithms. New families of soft LVQ and clustering algorithms are also derived by selecting nonlinear and logarithmic generator functions.